On sequential estimation of an autoregressive parameter
We study the estimation problem for the first-order autoregressive model The asymptotic behavior of the classical maximum likelihood estimator (MLE) (when the number of observation n tends to infinity) differs essentially between the cases of stable, near stable and explosive models. The main result...
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| Published in | Stochastics and stochastics reports Vol. 60; no. 3-4; pp. 219 - 240 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Gordon and Breach Science Publishers
01.04.1997
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1045-1129 |
| DOI | 10.1080/17442509708834107 |
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| Abstract | We study the estimation problem for the first-order autoregressive model
The asymptotic behavior of the classical maximum likelihood estimator (MLE)
(when the number of observation n tends to infinity) differs essentially between the cases of stable, near stable and explosive models.
The main result of the paper claims the possibility to obtain the universal standard normal limit distribution making use of the random normalizing factor
for the divergence
where N is a proper stopping time |
|---|---|
| AbstractList | We study the estimation problem for the first-order autoregressive model
The asymptotic behavior of the classical maximum likelihood estimator (MLE)
(when the number of observation n tends to infinity) differs essentially between the cases of stable, near stable and explosive models.
The main result of the paper claims the possibility to obtain the universal standard normal limit distribution making use of the random normalizing factor
for the divergence
where N is a proper stopping time |
| Author | Shiryaev, A.N. Spokoiny, V.G. |
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| CitedBy_id | crossref_primary_10_1080_07474946_2016_1275421 crossref_primary_10_1214_aos_1013203463 crossref_primary_10_1016_j_jspi_2006_10_007 crossref_primary_10_1016_S0047_259X_03_00081_2 crossref_primary_10_1016_S0167_7152_99_00121_2 crossref_primary_10_2139_ssrn_2311139 crossref_primary_10_1016_S0304_4149_02_00120_5 crossref_primary_10_1017_S0266466616000529 crossref_primary_10_1080_07474940008836438 crossref_primary_10_1080_0747940500452213 crossref_primary_10_1081_SQA_120022082 crossref_primary_10_1080_07474940500310932 crossref_primary_10_1081_SQA_120022081 |
| Cites_doi | 10.1007/978-1-4612-5505-5 10.1214/aos/1176346154 10.1111/j.2517-6161.1953.tb00121.x 10.1137/S0040585X9798662X 10.1214/aos/1176347634 10.1214/aos/1176344077 10.2307/1905674 10.1214/aoms/1177706450 10.1214/aos/1176346057 10.1214/aos/1176345591 10.1214/aoms/1177706198 10.1214/aos/1176350492 10.1080/17442508608833405 10.1214/aos/1176350711 10.1214/aos/1176350962 |
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| Snippet | We study the estimation problem for the first-order autoregressive model
The asymptotic behavior of the classical maximum likelihood estimator (MLE)
(when the... |
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| SubjectTerms | 1991 Mathematics Subject Classification: 62L12, 62M10 Autoregressive parameter least square estimator maximum likelihood estimator sequential estimation stopping time |
| Title | On sequential estimation of an autoregressive parameter |
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